Which of the following numbers is a factor of 132? ${4,7,9,10,14}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $132$ by each of our answer choices. $132 \div 4 = 33$ $132 \div 7 = 18\text{ R }6$ $132 \div 9 = 14\text{ R }6$ $132 \div 10 = 13\text{ R }2$ $132 \div 14 = 9\text{ R }6$ The only answer choice that divides into $132$ with no remainder is $4$ $ 33$ $4$ $132$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $4$ are contained within the prime factors of $132$ $132 = 2\times2\times3\times11 4 = 2\times2$ Therefore the only factor of $132$ out of our choices is $4$. We can say that $132$ is divisible by $4$.